[10]
/(°)
-70.5
-65.03
-78.46
-67.51
-57.9
-62
-58
-58.3
0.87
0.644
1.074
0.787
0.69
0.65
0.68
0.483 As can be seen from Table 1, the crack angle and fracture toughness ratio of pure Mode II are located in among several other theories, and close to the measured values. I, II mixed mode crack. The crack angle of I, II mixed mode crack. Because of the heterogeneous nature of concrete, there are many inevitable defects in its inner, such as tiny cracks and holes. When the force reaches a certain load value, the defects distributed randomly in concrete began to expand. Tensile strength of the concrete is very weak, under which deficiencies will expand faster and be more obvious. In this paper, we use the fracture mechanics to analysis concrete crack propagation problems, the simplified model is showed in Figure (2) below. Figure 2 micro-cracks analysis model Figure 3 inclined crack in tension In order to facilitate the analysis, the simplified model in Figure (2) was randomly removed one-way inclined crack, zoomed in Figure (3) shows, in this moment, the stress intensity factor near the inclined crack tip is: (20) Where, a is half the length of crack, is the angle between the crack and the vertical. Substitute (20) into (7), we obtain: (21) Equation (21) is relationship equation of the strain-energy theory of Iso- line in concrete about the crack angle and the crack inclination angle , which can be drawn from the curve of the crack inclination angle and the crack angle when an infinite plane center one-way tensile inclined crack, shown in Figure (4). Compared with the tensile stress theory, strain energy theory and experimental data, It can be concluded that when, the theory of this curve and the tensile stress, strain energy density factor theory are close to each other. In addition, this curve fits very well with the measured values, when compared with the measured results from the shows. Figure 4: Relationship curve about and Figure 5: The curve of fracture criterion The theory values of critical fracture curve compared with the measured values. The relationship of mixed mode fracture andcan be obtained by equation (17): (22) Now the values of mixed mode fracture and derived from formula (22) are plotted in Figure 4, in order to facilitate comparative analysis, and has been on the concrete I, III mixed mode fracture criterion and a large number of experimental studies testing the values drawing in Figure 4 together. It can be seen from the figure that this theory are very close to the tensile strain theory and experimental data. Conclusions Concrete is a brittle material constituted by the sand, gravel, cement and others, but the destruction process is not as simple as the brittle material because of its homogenization and non-linearity. There are many natural micro-pores and micro-cracks in its inner, as to a certain extent by the tension, the original defects crack, and then crack continues to expand, go through, and eventually leads to unstable fracture of concrete. Based on the analysis of existing fracture criterion theories and some experimental data, this paper proposed the strain energy criterion of Iso- line for mixed mode crack in concrete. This paper established Iso-line strain energy criterion formula, which is easier, clear in physical concept, convenient for engineering applications. Both Figure (4) and Figure (5) show that the theoretical predictions and the measured values of I, II mixed mode crack fracture of the critical and and~ are consistent, indicating that the theory is suitable for concrete materials. Acknowledgements This work was financially supported by the Liaoning Province Education Administration Foundation (L2010393). References
Google Scholar
[1]
Xiaozhong Yu. Experimental research and numerical simulation the crack propagation process of concrete I-II mixed mode fracture initiation criterion. Journal of Hydraulic Engineering, 1982(6): 27-37. (In Chinese)
Google Scholar
[2]
Beilei Hu, Guofan Zhao. The effective fracture criterion for concrete I, II mixed mode crack. 1996(6): 776-781. (In Chinese)
Google Scholar
[3]
F Erdogan, G. C Sih. On crack extension in plates under plane loading and transverse shear [J]. Trans. ASME, Journal of Basic Engng, 1963, 85:519~527.
DOI: 10.1115/1.3656898
Google Scholar
[4]
R J Nuismer. An energy release rate criterion for mixed mode fracture [J]. Int Jour. Fract. Mech. 1975, 11(2):245~250.
DOI: 10.1007/bf00038891
Google Scholar
[5]
G C Sih. Energy-density concept in fracture mechanics [J]. Engng. Fracture Mech, 1973, 5: 1037~1040.
DOI: 10.1016/0013-7944(73)90072-6
Google Scholar
[6]
Sili Chen. The strain energy criterion of Iso-W line for mixed mode crack. Journal of Shenyang University of Technology, 1992(3): 65-68. (In Chinese)
Google Scholar
[7]
Daoyuan Xu. Testing research the fracture criterion of concrete I, II mixed mode crack determined by four-point shear test. 1984(9):19~23. (In Chinese)
Google Scholar
[8]
Daoyuan Xu. Testing research the critical fracture curves of concrete I, II mixed mode crack. Concrete and aerated concrete, 1983(6):21~25. (In Chinese)
Google Scholar
[9]
Daoyuan Xu. Discussion of Concrete I, II mixed mode fracture criterion. Journal of Hydraulic Engineering, 1982(6): 20~24. (In Chinese)
Google Scholar
[10]
Kaiqi Long. Computational and experimental research the fracture criterion for concrete I, II mixed mode crack. Shannxi hydropower, 1989(2):51~61. (In Chinese)
Google Scholar
